Mike,
Your new suggested criterion is failed by anything that meets both of
the Plurality
and Minimal Defense criteria.
27: A>B
24: B (sincere might be B>A)
49: C
Together they say that B must win here, but your suggested criterion
says that B can do
no better than tie with A,
The only 2 methods I can think of that for sure meet your suggested
criterion are IRV (aka Alternative Vote)
and MMPO.
It is for sure failed by SMD,TR (the method you're calling DP) even
though that fails Plurality.
It disqualifies both A and C. If the B voters had sincerely middle-rated
A then only C would have
been disqualified and A would have won.
Chris Benham
Mike Ossipoff wrote (2 Nov 2011):
First I proposed CD, then I said that it might be too demanding, and
_tentatively_
suggested a replacement. It wasn't a good one.
Here I suggest another replacement for CD:
Tentative replacement for CD:
Supporting definitions:
"The A voters" are the voters to whom A is favorite.
"The B voters" are the voters to whom B is favorite.
"The others" are the candidates other than A and B.
A voter votes sincerely iff s/he doesn't falsify a preference or
fail to vote a preference that the voting system in use would have
allowed hir to vote in addition to those preferences that s/he actually
did vote.
Premise:
The A voters and the B voters are, together, a majority.
They all prefer A and B to the others.
Voting is sincere, except that the B voters refuse to vote A over anyone.
A would win under sincere voting (in other words, had the B voters
voted sincerely
as did everyone else).
Requirement:
Either A wins, or A and B win (tie), or neither A nor B wins.
[end of tentative CD definition]
I know that I don't like what happens in the ABE. Maybe this
replacement, today,
is the way to describe ABE with a criterion.
Mike Ossipoff
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